Mathematical foundations of navigation parameters of the air transport by magnetominal circulation by using the method of least squares

Modern processes of air traffic control are realized on a single information platform called globally-localized information clusters, which are united in a single information environment. The main information component for such a system is navigation information about the location of each aircraft, containing dynamically updated data on its current coordinates and motion parameters. Under such conditions, there is the task of integrating navigation information obtained from various information sources that make up the aircraft avionics. Traditional approaches do not provide joint smoothing of coordinate information invariant to synchronization of measurements; therefore, the statistical analysis of experimental samples of navigation parameters is determined by the object of research. The paper deals with a mathematical apparatus for providing multidimensional smoothing of the navigation parameters of an aircraft using the least squares method. To implement the proposed approach, the method of affine mapping of the coordinate space is used. This provides independent functional dependencies of the coordinate field of the aircraft for their joint processing by the method of least squares. The developed software for multidimensional smoothing of the navigation parameters of the aircraft can be used to study the processes of evolution and maintenance of the software of the on-board computer complex of the aircraft. A feature of the approach is the time coordination of the obtained measurements at the model level, reduces the requirements for synchronization of the primary navigation parameters and expands the possibilities in the list of parameters that are processed together. This provides an increase in the accuracy of determining the current position of the aircraft compared to traditional approaches by attracting additional data redundancy. The proposed approach can be extended to a wide range of applied industries related to the measurement, evaluation and prediction of changes over time in interrelated processes.